Black Holes by John Percy, University of Toronto
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Negreiros Lecture II
General Relativity and Neutron Stars - II Rodrigo Negreiros – UFF - Brazil Outline • Compact Stars • Spherically Symmetric • Rotating Compact Stars • Magnetized Compact Stars References for this lecture Compact Stars • Relativistic stars with inner structure • We need to solve Einstein’s equation for the interior as well as the exterior Compact Stars - Spherical • We begin by writing the following metric • Which leads to the following components of the Riemman curvature tensor Compact Stars - Spherical • The Ricci tensor components are calculated as • Ricci scalar is given by Compact Stars - Spherical • Now we can calculate Einstein’s equation as 휇 • Where we used a perfect fluid as sources ( 푇휈 = 푑푖푎푔(휖, 푃, 푃, 푃)) Compact Stars - Spherical • Einstein’s equation define the space-time curvature • We must also enforce energy-momentum conservation • This implies that • Where the four velocity is given by • After some algebra we get Compact Stars - Spherical • Making use of Euler’s equation we get • Thus • Which we can rewrite as Compact Stars - Spherical • Now we introduce • Which allow us to integrate one of Einstein’s equation, leading to • After some shuffling of Einstein’s equation we can write Summary so far... Metric Energy-Momentum Tensor Einstein’s equation Tolmann-Oppenheimer-Volkoff eq. Relativistic Hydrostatic Equilibrium Mass continuity Stellar structure calculation Microscopic Ewuation of State Macroscopic Composition Structure Recapitulando … “Feed” with diferente microscopic models Microscopic Ewuation of State Macroscopic Composition Structure Compare predicted properties with Observed data. Rotating Compact Stars • During its evolution, compact stars may acquire high rotational frequencies (possibly up to 500 hz) • Rotation breaks spherical symmetry, increasing the degrees of freedom. -
Exploring Pulsars
High-energy astrophysics Explore the PUL SAR menagerie Astronomers are discovering many strange properties of compact stellar objects called pulsars. Here’s how they fit together. by Victoria M. Kaspi f you browse through an astronomy book published 25 years ago, you’d likely assume that astronomers understood extremely dense objects called neutron stars fairly well. The spectacular Crab Nebula’s central body has been a “poster child” for these objects for years. This specific neutron star is a pulsar that I rotates roughly 30 times per second, emitting regular appar- ent pulsations in Earth’s direction through a sort of “light- house” effect as the star rotates. While these textbook descriptions aren’t incorrect, research over roughly the past decade has shown that the picture they portray is fundamentally incomplete. Astrono- mers know that the simple scenario where neutron stars are all born “Crab-like” is not true. Experts in the field could not have imagined the variety of neutron stars they’ve recently observed. We’ve found that bizarre objects repre- sent a significant fraction of the neutron star population. With names like magnetars, anomalous X-ray pulsars, soft gamma repeaters, rotating radio transients, and compact Long the pulsar poster child, central objects, these bodies bear properties radically differ- the Crab Nebula’s central object is a fast-spinning neutron star ent from those of the Crab pulsar. Just how large a fraction that emits jets of radiation at its they represent is still hotly debated, but it’s at least 10 per- magnetic axis. Astronomers cent and maybe even the majority. -
Exploring Exoplanet Populations with NASA's Kepler Mission
SPECIAL FEATURE: PERSPECTIVE PERSPECTIVE SPECIAL FEATURE: Exploring exoplanet populations with NASA’s Kepler Mission Natalie M. Batalha1 National Aeronautics and Space Administration Ames Research Center, Moffett Field, 94035 CA Edited by Adam S. Burrows, Princeton University, Princeton, NJ, and accepted by the Editorial Board June 3, 2014 (received for review January 15, 2014) The Kepler Mission is exploring the diversity of planets and planetary systems. Its legacy will be a catalog of discoveries sufficient for computing planet occurrence rates as a function of size, orbital period, star type, and insolation flux.The mission has made significant progress toward achieving that goal. Over 3,500 transiting exoplanets have been identified from the analysis of the first 3 y of data, 100 planets of which are in the habitable zone. The catalog has a high reliability rate (85–90% averaged over the period/radius plane), which is improving as follow-up observations continue. Dynamical (e.g., velocimetry and transit timing) and statistical methods have confirmed and characterized hundreds of planets over a large range of sizes and compositions for both single- and multiple-star systems. Population studies suggest that planets abound in our galaxy and that small planets are particularly frequent. Here, I report on the progress Kepler has made measuring the prevalence of exoplanets orbiting within one astronomical unit of their host stars in support of the National Aeronautics and Space Admin- istration’s long-term goal of finding habitable environments beyond the solar system. planet detection | transit photometry Searching for evidence of life beyond Earth is the Sun would produce an 84-ppm signal Translating Kepler’s discovery catalog into one of the primary goals of science agencies lasting ∼13 h. -
Get Outside What to Look for in the Summer Sky Your Hosts of the Summer Sky Are Three Bright Stars — Vega, Altair and Deneb
Get Outside What to Look for in the Summer Sky Your hosts of the summer sky are three bright stars — Vega, Altair and Deneb. Together they make up the Summer Triangle. Look for the triangle in the east on a June evening, moving NORTH to overhead as the season progresses. Polaris The Big Dipper Deneb Cygnus Vega Lyra Hercules Arcturus EaST West Summer Triangle Altair Aquila Sagittarius Antares Turn the map so Scorpius the direction you are facing is at the Teapot the bottom. south facebook.com/KidsCanBooks @KidsCanPress GET OUTSIDE Text © 2013 Jane Drake & Ann Love Illustrations © 2013 Heather Collins www.kidscanpress.com Get Outside Vega The Keystone The brightest star in the Between Vega and Arcturus, Summer Triangle, Vega is look for four stars in a wedge or The summer bluish white. It is in the keystone shape. This is the body solstice constellation Lyra, the Harp. of Hercules, the Strongman. His feet are to the north and Every day from late Altair his arms to the south, making December to June, the The second-brightest star in his figure kneel Sun rises and sets a little the triangle, Altair is white. upside down farther north along the Altair is in the constellation in the sky. horizon. But about June Aquila, the Eagle. 21, the Sun seems to stop Keystone moving north. It rises in Deneb the northeast and sets in The dimmest star of the the northwest, seemingly Summer Triangle, Deneb would in the same spots for be the brightest if it were not so Hercules several days. -
Enhanced Mass Loss Rates in Red Supergiants and Their Impact in The
Revista Mexicana de Astronom´ıa y Astrof´ısica, 55, 161–175 (2019) DOI: https://doi.org/10.22201/ia.01851101p.2019.55.02.04 ENHANCED MASS LOSS RATES IN RED SUPERGIANTS AND THEIR IMPACT ON THE CIRCUMSTELLAR MEDIUM L. Hern´andez-Cervantes1,2, B. P´erez-Rend´on3, A. Santill´an4, G. Garc´ıa-Segura5, and C. Rodr´ıguez-Ibarra6 Received September 25 2018; accepted May 8 2019 ABSTRACT In this work, we present models of massive stars between 15 and 23 M⊙, with enhanced mass loss rates during the red supergiant phase. Our aim is to explore the impact of extreme red supergiant mass-loss on stellar evolution and on their cir- cumstellar medium. We computed a set of numerical experiments, on the evolution of single stars with initial masses of 15, 18, 20 and, 23 M⊙, and solar composi- tion (Z = 0.014), using the numerical stellar code BEC. From these evolutionary models, we obtained time-dependent stellar wind parameters, that were used ex- plicitly as inner boundary conditions in the hydrodynamical code ZEUS-3D, which simulates the gas dynamics in the circumstellar medium (CSM), thus coupling the stellar evolution to the dynamics of the CSM. We found that stars with extreme mass loss in the RSG phase behave as a larger mass stars. RESUMEN En este trabajo presentamos modelos evolutivos de estrellas en el intervalo de 15 a 23 M⊙, usando un incremento en la tasa de p´erdida de masa durante su fase de supergigante roja para explorar el impacto de una fuerte p´erdida de masa en la evoluci´on de la estrella y en la din´amica de su medio circunestelar. -
Multiwavelength Observations of Accretion in Low-Mass X-Ray Binary Systems Robert I
1 Multiwavelength Observations of Accretion in Low-Mass X-ray Binary Systems Robert I. Hynesa Abstract This work is intended to provide an introduction to multiwavelength observations of low-mass X-ray binaries and the techniques used to ana- lyze and interpret their data. The focus will primarily be on ultraviolet, optical, and infrared observations and their connections to other wave- lengths. The topics covered include: outbursts of soft X-ray transients, accretion disk spectral energy distributions, orbital lightcurves in lumi- nous and quiescent states, super-orbital and sub-orbital variability, line spectra, system parameter determinations, and echo-mapping and other rapid correlated variability. 1.1 Introduction The first X-ray binary to be observed and identified as such was Scorpius X-1 (Giacconi et al., 1962), although several other systems were known as optical stars or novae before this. Within a few years, optical and radio counterparts to Sco X-1 were discovered (Sandage et al., 1966; Andrew and Purton, 1968), and the topic has remained multiwavelength in nature since then. This work is intended to provide an introduction to some of the obser- vational characteristics of X-ray binaries suitable for a graduate student or an advanced undergraduate. My aim was to produce a primer for someone relatively new to the field rather than a comprehensive review. Where appropriate I will also discuss techniques for analysis and inter- a Louisiana State University, Department of Physics and Astronomy, 202 arXiv:1010.5770v1 [astro-ph.HE] 27 Oct 2010 Nicholson Hall, Tower Drive, Baton Rouge, LA 70803, USA 2 R. -
Astro 210 Lecture 37 April 23, 2018 Announcements
Astro 210 Lecture 37 April 23, 2018 Announcements: • HW 11: The Final Frontier posted, due 5:00pm Friday • Grades: we are catching up! keep checking Moodle 1 Last Time: Searching for Black Holes Black holes themselves are invisible∗ can can detect them via their strong gravitational effects on their close surroundings example: binary stars X-rays emitted from unseen massive companion ∗this ignores Hawking radiation–see below 2 Our Own Galactic Center central ∼ 30 pc of Galaxy: can’t see optically (Q: why?), but can in other wavelengths: extended (non-point) radio emission (Sagittarius A) from high-energy electrons radio source at center: Sgr A∗ size 2.4 AU(!), variable emission in radio, X-ray www: X-ray Sgr A∗ in infrared wavelengths: can see stars near Sgr A∗ and they move! www: Sgr A∗ movie elliptical paths! closest: period P = 15.2 yr semi-major axis: a = 4.64 × 10−3 pc 3 6 → enclosed mass (3.7 ± 1.5) × 10 M⊙ Q: and so? the center of our Galaxy contains a black hole! Sgr A∗ Schwarzschild radius 7 −7 rSch = 1.1 × 10 km=0.74 AU = 3.6 × 10 pc (1) → not resolved (yet) but: Event Horizon Telescope has data and right now is processing possible first images! Galactic black hole raises many questions: • how did it get there? • Sgr A∗ low luminosity, “quiet” compared to more “active” galactic nuclei www: AGN: M87 why? open question.... • in last few months: discovery of high-energy “bubbles” 4 above & below Galactic center www: gamma-ray images → remains of the most recent Sgr A∗ belch? Galaxies and Black Holes The Milky Way is not the only -
Arxiv:Gr-Qc/0612030 V1 5 Dec 2006
December 6, 2006 1:49 WSPC - Proceedings Trim Size: 9.75in x 6.5in main 1 STABLE DARK ENERGY STARS: AN ALTERNATIVE TO BLACK HOLES? FRANCISCO S. N. LOBO Centro de Astronomia e Astrof´ısica da Universidade de Lisboa, Campo Grande, Ed. C8 1749-016 Lisboa, Portugal flobo@cosmo.fis.fc.ul.pt In this work, a generalization of the Mazur-Mottola gravastar model is explored, by considering a matching of an interior solution governed by the dark energy equation of state, ω ≡ p/ρ < −1/3, to an exterior Schwarzschild vacuum solution at a junction interface, situated near to where the event horizon is expected to form. The motivation for implementing this generalization arises from the fact that recent observations have confirmed an accelerated cosmic expansion, for which dark energy is a possible candidate. Keywords: Gravastars; dark energy. Although evidence for the existence of black holes is very convincing, a certain amount of scepticism regarding the physical reality of singularities and event hori- zons is still encountered. In part, due to this scepticism, an alternative picture for the final state of gravitational collapse has emerged, where an interior compact ob- ject is matched to an exterior Schwarzschild vacuum spacetime, at or near where the event horizon is expected to form. Therefore, these alternative models do not possess a singularity at the origin and have no event horizon, as its rigid surface is arXiv:gr-qc/0612030 v1 5 Dec 2006 located at a radius slightly greater than the Schwarzschild radius. In particular, the gravastar (gravitational vacuum star) picture, proposed by Mazur and Mottola,1 has an effective phase transition at/near where the event horizon is expected to form, and the interior is replaced by a de Sitter condensate. -
Active Galactic Nuclei: a Brief Introduction
Active Galactic Nuclei: a brief introduction Manel Errando Washington University in St. Louis The discovery of quasars 3C 273: The first AGN z=0.158 2 <latexit sha1_base64="4D0JDPO4VKf1BWj0/SwyHGTHSAM=">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</latexit> <latexit sha1_base64="H7Rv+ZHksM7/70841dw/vasasCQ=">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</latexit> The power source of quasars • The luminosity (L) of quasars, i.e. how bright they are, can be as high as Lquasar ~ 1012 Lsun ~ 1040 W. • The energy source of quasars is accretion power: - Nuclear fusion: 2 11 1 ∆E =0.007 mc =6 10 W s g− -
Summer Constellations
Night Sky 101: Summer Constellations The Summer Triangle Photo Credit: Smoky Mountain Astronomical Society The Summer Triangle is made up of three bright stars—Altair, in the constellation Aquila (the eagle), Deneb in Cygnus (the swan), and Vega Lyra (the lyre, or harp). Also called “The Northern Cross” or “The Backbone of the Milky Way,” Cygnus is a horizontal cross of five bright stars. In very dark skies, Cygnus helps viewers find the Milky Way. Albireo, the last star in Cygnus’s tail, is actually made up of two stars (a binary star). The separate stars can be seen with a 30 power telescope. The Ring Nebula, part of the constellation Lyra, can also be seen with this magnification. In Japanese mythology, Vega, the celestial princess and goddess, fell in love Altair. Her father did not approve of Altair, since he was a mortal. They were forbidden from seeing each other. The two lovers were placed in the sky, where they were separated by the Celestial River, repre- sented by the Milky Way. According to the legend, once a year, a bridge of magpies form, rep- resented by Cygnus, to reunite the lovers. Photo credit: Unknown Scorpius Also called Scorpio, Scorpius is one of the 12 Zodiac constellations, which are used in reading horoscopes. Scorpius represents those born during October 23 to November 21. Scorpio is easy to spot in the summer sky. It is made up of a long string bright stars, which are visible in most lights, especially Antares, because of its distinctly red color. Antares is about 850 times bigger than our sun and is a red giant. -
Star Maps: Where Are the Black Holes?
BLACK HOLE FAQ’s 1. What is a black hole? A black hole is a region of space that has so much mass concentrated in it that there is no way for a nearby object to escape its gravitational pull. There are three kinds of black hole that we have strong evidence for: a. Stellar-mass black holes are the remaining cores of massive stars after they die in a supernova explosion. b. Mid-mass black hole in the centers of dense star clusters Credit : ESA, NASA, and F. Mirabel c. Supermassive black hole are found in the centers of many (and maybe all) galaxies. 2. Can a black hole appear anywhere? No, you need an amount of matter more than 3 times the mass of the Sun before it can collapse to create a black hole. 3. If a star dies, does it always turn into a black hole? No, smaller stars like our Sun end their lives as dense hot stars called white dwarfs. Much more massive stars end their lives in a supernova explosion. The remaining cores of only the most massive stars will form black holes. 4. Will black holes suck up all the matter in the universe? No. A black hole has a very small region around it from which you can't escape, called the “event horizon”. If you (or other matter) cross the horizon, you will be pulled in. But as long as you stay outside of the horizon, you can avoid getting pulled in if you are orbiting fast enough. 5. What happens when a spaceship you are riding in falls into a black hole? Your spaceship, along with you, would be squeezed and stretched until it was torn completely apart as it approached the center of the black hole. -
Undergraduate Thesis on Supermassive Black Holes
Into the Void: Mass Function of Supermassive Black Holes in the local universe A Thesis Presented to The Division of Mathematics and Natural Sciences Reed College In Partial Fulfillment of the Requirements for the Degree Bachelor of Arts Farhanul Hasan May 2018 Approved for the Division (Physics) Alison Crocker Acknowledgements Writing a thesis is a long and arduous process. There were times when it seemed further from my reach than the galaxies I studied. It’s with great relief and pride that I realize I made it this far and didn’t let it overpower me at the end. I have so many people to thank in very little space, and so much to be grateful for. Alison, you were more than a phenomenal thesis adviser, you inspired me to believe that Astro is cool. Your calm helped me stop freaking out at the end of February, when I had virtually no work to show for, and a back that ached with every step I took. Thank you for pushing me forward. Working with you in two different research projects were very enriching experiences, and I appreciate you not giving up on me, even after all the times I blanked on how to proceed forward. Thank you Johnny, for being so appreciative of my work, despite me bringing in a thesis that I myself barely understood when I brought it to your table. I was overjoyed when I heard you wanted to be on my thesis board! Thanks to Reed, for being the quirky, intellectual community that it prides itself on being.